Question

$C_P-C_V=R$. Is the given statement

• A. True
• B. False

Answer 1

The correct option is A

True

The enthalpy for one mole of ideal gas can be given as:
$H=U+PV$
and we know that,
PV = RT for 1 mole of gas
$\therefore H=U+RT$
Now by differentiating the above equation with respect to temperature we get:
$\therefore \frac{dH}{dT}=\frac{dU}{dT}+R{C}_P=(\frac{dH}{dT}{)}_P{C}_V=(\frac{dU}{dT}{)}_V$
$\therefore C_P=C_V+R$
$\therefore C_P-C_V=R$